Question

What is the value of y in the solutions of the system of equations: 3x + 4y = 3 and 2x – 4y = 12?

Answer 1

Step-by-step explanation:
Step 1) Solve the second equation for
y
2
x
+
y
=
−
8
−
2
x
+
2
x
+
y
=
−
2
x
−
8
0
+
y
=
−
2
x
−
8
y
=
−
2
x
−
8
Step 2) Substitute
(
−
2
x
−
8
)
for
y
in the first equation and solve for
x
:
−
3
x
+
4
y
=
12
becomes:
−
3
x
+
4
(
−
2
x
−
8
)
=
12
−
3
x
+
(
4
×
−
2
x
)
+
(
4
×
−
8
)
=
12
−
3
x
+
(
−
8
x
)
+
(
−
32
)
=
12
−
3
x
−
8
x
−
32
=
12
(
−
3
−
8
)
x
−
32
=
12
−
11
x
−
32
=
12
−
11
x
−
32
+
32
=
12
+
32
−
11
x
−
0
=
44
−
11
x
=
44
−
11
x
−
11
=
44
−
11
−
11
x
−
11
=
−
4
x
=
−
4
Step 3) Substitute
−
4
for
x
in the solution to the second equation at the end of Step 1 and calculate
y
:
y
=
−
2
x
−
8
becomes:
y
=
(
−
2
×
−
4
)
−
8
y
=
8
−
8
y
=
0
The Solution Is:
x
=
−
4
and
y
=
0
Or
(
−
4
,
0
)

Answer 2

y = -3

Step-by-step explanation:

3x + 4y = 3

2x - 4y = 12

5x = 15 Add the two equation together because the y terms are

opposite each other and goes out when you add the equations

x = 5

Substitute into the first equation and solve for y when x = 5

3x + 4y = 3

3(5) + 4y = 3

15 + 4y = 3

4y = 3 - 15

4y = -12

y = -3